They are taking the government to the European Court of Human Rights in a bid to end the system of male primogeniture which has resulted in almost all titles being passed to male heirs, the BBC reported.
The five women, who are part of the Daughters' Rights campaign, want the UK government to remove the word "male" from legislation they describe as "outdated" so they can stand for by-elections to the Lords.
The group accuse the government of "double standards" because it promotes women's rights.
The five women involved in the case are: Lady Willa Franks, eldest daughter of the Earl of Balfour; Lady Eliza Dundas, eldest daughter of the Earl of Ronaldshay; Sarah Long, elder sister to the current Viscount Long of Wraxall; Tanya Field, eldest daughter of the Earl of Macclesfield, and Hatta Byng, eldest daughter of Viscount Torrington.
New rules on royal succession came into force in 2015 to remove male bias, meaning that Princess Charlotte is currently fourth in line to the throne.
UK courts do not have oversight over the rules governing parliamentary procedure, the BBC report said.
Solicitor Paul Hardy, from law firm DLA Piper which is bringing the case, said the application to the European Court of Human Rights "raises profound questions about sexual equality and membership of the House of Lords".
The barrister for the campaign, Edward Legard, said: "It seems wrong in a country where women, including now royal women, are born with equal opportunities, that we continue to discriminate against one group based only on gender." PTI AKJ AKJ
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